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Volume 23, Issue 1
Superconvergence of Tetrahedral Quadratic Finite Elements

Jan Brandts & Michal Křížek

J. Comp. Math., 23 (2005), pp. 27-36.

Published online: 2005-02

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  • Abstract

For a model elliptic boundary value problem we will prove that on strongly regular families of uniform tetrahedral partitions of a pohyhedral domain, the gradient of the quadratic finite element approximation is superclose to the gradient of the quadratic Lagrange interpolant of the exact solution. This supercloseness will be used to construct a post-processing that increases the order of approximation to the gradient in the global $L^2$-norm.

  • Keywords

Tetrahedron, Superconvergence, Supercloseness, Post-processing, Gauss points.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-23-27, author = {Brandts , Jan and Křížek , Michal}, title = {Superconvergence of Tetrahedral Quadratic Finite Elements}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {1}, pages = {27--36}, abstract = {

For a model elliptic boundary value problem we will prove that on strongly regular families of uniform tetrahedral partitions of a pohyhedral domain, the gradient of the quadratic finite element approximation is superclose to the gradient of the quadratic Lagrange interpolant of the exact solution. This supercloseness will be used to construct a post-processing that increases the order of approximation to the gradient in the global $L^2$-norm.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8793.html} }
TY - JOUR T1 - Superconvergence of Tetrahedral Quadratic Finite Elements AU - Brandts , Jan AU - Křížek , Michal JO - Journal of Computational Mathematics VL - 1 SP - 27 EP - 36 PY - 2005 DA - 2005/02 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8793.html KW - Tetrahedron, Superconvergence, Supercloseness, Post-processing, Gauss points. AB -

For a model elliptic boundary value problem we will prove that on strongly regular families of uniform tetrahedral partitions of a pohyhedral domain, the gradient of the quadratic finite element approximation is superclose to the gradient of the quadratic Lagrange interpolant of the exact solution. This supercloseness will be used to construct a post-processing that increases the order of approximation to the gradient in the global $L^2$-norm.

Brandts , Jan and Křížek , Michal. (2005). Superconvergence of Tetrahedral Quadratic Finite Elements. Journal of Computational Mathematics. 23 (1). 27-36. doi:
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